What is the fastest amount of time a technologically advanced species can evolve?

I am creating a hypothetical race of aliens native to a planet orbiting an F class star; the mass of the star is 1.50 (M☉). Would this star live long enough to allow the evolution of intelligent life on a planet orbiting it?

TL;DR
If your aliens evolved on the same timescales as Earth life, then no; we took 2 to 3 Ga too long. If we assume selection pressures drove the alien microbes to much faster evolution, then yes; you've got anywhere from 1 Ga of wiggle room to life forming just before armageddon comes. (Ga is Giga-annum, or a billion years.)

Lifespan of a Star
This forum post links us to this article about worldbuilding and star ages. It lists several types of F-class stars, ranging in lifespans between 1.6 and 6.9 Ga. Using the data on the tables, we get a graph like this:

Mass vs Age w/ exponential trend line.

The blue line with the dots is the data from that page. It's clearly not enough sample points to get a good trendline (the green one), but I tried anyways. The best fit is exponential decay, about $l=609e^{-3.76m}$, where $m$ is mass in solar masses, and $l$ is lifespan in gigayears. Using that formula, we see that an F-class star of 1.5 M☉ has a lifespan of about 2.16 Ga.

Not liking 4 data points much, I added all 31 data points from the page:

Mass vs Age w/ exponential trend line.

Mass vs Age w/ power trend line, zoomed in.

The first image includes all 31 data points, keeping the exponential decay trendline, which obviously sucks as an approximation now. The second image is zoomed in a bit so we can see the relevant part of the graph better, and I switched to a power function. The power function isn't perfect, but fits the data range better. Using $l=5.577m^{-2.044}$, we get a lifespan of about 2.43 Ga.

Later in the forum post, a guy gives the equation $l=10m^{-2}$ as an approximation, which is the red trendline in the second graph. Using it gives a lifespan of 4.44 Ga. Something he points out is that these numbers are only the stable lifetime of the star, and the planet will realistically be in the habitable zone for about half of it.

Formation of Life
Planets tend to form about the same time the star does, out of the same accretion disc (a couple millions years after star formation). Once the planet has formed though, it's really hot, both from the initial gravitational collapse of the solar accretion disc and from the planetary formation process which involves the planet running into stuff at high speeds and collecting that stuff. So we need a long time for the planet to get cool enough that any kind of life can survive. On Earth, it took 0.5 to 1 Ga before the first life formed, though I would expect a smaller planet that formed farther from the star to cool down more quickly.

Next, the single-celled life needs to evolve into complex organisms. Here's a cool graph of Earth's life history:

History of Earth life. Source

This says it took about 3.5 Ga just to get multicellular life. Then another 1.5 Ga to get humans. Still, Earth is a sample size of one, making it imprudent to try drawing sweeping statistical inferences from our single timeline.

According to Wikipedia, researchers were able to force single-celled to multi-celled evolution in a laboratory. From there, it seems plausible for a planet to exist where conditions forced selection on single-celled organisms at a greater rate, speeding up the first stages of life.

The Cambrian explosion was about 0.5 Ga ago, and dramatically increased the diversity of life on Earth. If first life to the alien's explosion happened in something like 0.5 Ga, and evolution since the explosion happened more rapidly than on Earth, you could have intelligent life orbiting an F-class star.

A Note on the Habitable Zone
So our F-type star lasts 2 to 4 Ga, and our planet will be in the habitable zone for 1 to 2 Ga. We need 0.5 to 1 Ga for the planet to cool down, but we can ignore that if the planet was outside the habitable zone to start with.

Habitable Zone

When the star forms, the area near the star (the red zone) is too hot for life, and the area far from the star (the blue and green zones) is too cold for life. There's only a thin ring between the two (the orange zone) where life can form. As the star ages, it expands, pushing the habitable zone outward. Now, the orange zone is too hot, but the green zone (that was previously too cold) is just right.

If the planet (the purple dot) is at the right distance, the habitable zone will reach it just as it cools down to equilibrium with the energy from the star, giving life the best chance of succeeding.

Conclusion
- A planet outside the habitable zone cools down just as the habitable zone reaches it, giving around 1 to 2 Ga for intelligent life to form.
- Single-celled organisms could arise pretty quickly after that point. Perhaps several Ma.
- Single-celled organisms can evolve to multi-celled organisms in a lab, so there's not really a lower limit on that time frame. Perhaps a few Ma, perhaps a few hundred Ma.
- We don't know what caused the Cambrian explosion, so it's hard to make any claims about minimum times between multi-celled life and the explosion. Certainly less than 1 Ga, but perhaps a lot less. We could probably be safe with 0.5 Ga.
- From the explosion to intelligent life took about 0.5 Ga on Earth, though it could take less on our alien planet.

Adding that together, we get about 1 Ga on the lower end. So, using the short end of the star's potential lifespan, if life began almost immediately after the planet hit the habitable zone, and selection pressures drove the evolution of multicellular life shortly thereafter, and the aliens took half our time from their explosion to intelligent life, intelligent life would form right about the time the planet got too hot to support life.

Because we're talking geological timescales, you could twist this to fit your story however you want. Perhaps the aliens have millions of years between inventing space travel and the planet getting too hot so they're not too worried right now. Perhaps they have decades, and much of their populace has already succumbed to the heat; this is their last effort to save civilization as they know it!.

If we use the upper limit of the star's potential lifespan, we've got an extra billion years to play with, so anything's possible.

Not directly related to the question
An F-class star tends to be hotter and brighter than our Sun, but this article shows there's still a habitable zone, and fairly low UV radiation near the outer edge of it.

This article says 1.5 M☉ is the threshold for whether the star goes supergiant -> supernova or just giant -> nebula, which might be an interesting plot point for the end of the star's lifetime. Or not. Your call. :)

• I remember when I was researching this topic long time ago all I had was "two times the mass - one fifth of lifespan; half the mass - five times the lifespan" So do they still estimate based on observations, or did finally a formula emerge to calculate this in a proper way? Commented Feb 29, 2016 at 6:29
• If you stop writin "tldr" instead of "summary" I'll upvote it! Commented Feb 29, 2016 at 12:33
• use a smaller planet with proportionally less carbon and no moon, early life poisons it's own atmosphere much quicker by purifying the atmosphere(in human terms), mass die-offs cover the world in lipids and complex but dead molecules and multi cellular life steals the debris and reaches for the stars. Commented Dec 2, 2018 at 2:49
• Please explain what "Ga" is. Commented Feb 21, 2020 at 14:22